# Center of a Circle Calculator

Table of contents

How do I use the center of a circle calculator?How do I calculate the center of a circle?How do I find the center of a physical circle?Related calculatorsFAQsWelcome to the **center of a circle calculator** that finds the center of a circle for you. Here, we'll show you how to calculate the center of a circle from the various circle equations. We'll also cover finding the center of a circle without any math!

## How do I use the center of a circle calculator?

The **center of a circle calculator** is easy to use.

- Select the circle equation for which you have the values.
- Fill in the known values of the selected equation.
- You can find the center of the circle at the bottom.

Read on if you want to learn some formulas for the center of a circle!

## How do I calculate the center of a circle?

Circles can be defined with multiple equations. If you have a mathematical formula for your circle, pick the correct one from the headings below. We'll then explain how to calculate the center of the circle from there.

### The standard equation of a circle

The standard equation of a circle is:

where $C = r^2$, or the radius squared.

With this equation, we can **find the center of the circle** at point $(A, B)$. Be careful of the signs!

### The parametric equation of a circle

The parametric equation of a circle is defined as:

In this form, we can calculate the center of the circle as $(A,B)$ again.

### The general equation of a circle

A less common circle equation is the general equation of a circle:

In the general equation, we can calculate the center of the circle as $\left(-\frac{D}{2}, -\frac{E}{2}\right)$.

## How do I find the center of a physical circle?

If you have **a circle drawn on paper**, there's no center of a circle formula. Instead, follow these steps:

- Draw two (or more) chords on the circle.
- Find these chords' midpoints.
- From the midpoints, draw lines that are perpendicular to the chords.
- The point where these lines intersect is the circle's center.
- Congrats, you can find the center of the circle!

### What is the center of a circle represented by the equation (x+9)² + (y−6)² = 10²?

The center of this circle is `(−9, 6)`

, with a radius of `10`

. The equation `(x+9)² + (y−6)² = 10²`

is in the standard circle equation form `(x−A)² + (y−B)² = C`

, making `A = −9`

and `B = 6`

.

### What is the center of a circle represented by the equation (x−5)² + (y+6)² = 4²?

The center of this circle is `(5, −6)`

, with a radius of `4`

. The equation `(x−5)² + (y+6)² = 4²`

is in the standard circle equation form `(x−A)² + (y−B)² = C`

, making `A = 5`

and `B = −6`

.

### What is the center of a circle given the equation (x−5)² + (y+7)² = 81?

The center of this circle is `(5, −7)`

, with a radius of `√81 = 9`

. The equation `(x−5)² + (y+7)² = 81`

is in the standard circle equation form `(x−A)² + (y−B)² = C`

, making `A = 5`

and `B = −7`

.